Mode testing, critical bandwidth and excess mass

TL;DR

This paper introduces a new mode testing procedure that combines smoothing and excess mass methods, demonstrating improved practical performance over existing approaches with an application to philatelic data.

Contribution

A novel combined approach for mode testing that outperforms existing methods in practice, validated through simulations and real data.

Findings

New combined mode testing procedure shows superior performance.

Method outperforms existing procedures in practical scenarios.

Application to philatelic data illustrates real-world utility.

Abstract

The identification of peaks or maxima in probability densities, by mode testing or bump hunting, has become an important problem in applied fields. This task has been approached in the statistical literature from different perspectives, with the proposal of testing procedures which are based on kernel density estimators or on the quantification of excess mass. However, none of the existing proposals provides a satisfactory performance in practice. In this work, a new procedure which combines the previous approaches (smoothing and excess mass) is presented and compared with the existing methods, showing a superior behaviour. A real data example on philatelic data is also included for illustration purposes.